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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Model theory of difference fields
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by Zoé Chatzidakis and Ehud Hrushovski PDF
Trans. Amer. Math. Soc. 351 (1999), 2997-3071 Request permission


A difference field is a field with a distinguished automorphism $\sigma$. This paper studies the model theory of existentially closed difference fields. We introduce a dimension theory on formulas, and in particular on difference equations. We show that an arbitrary formula may be reduced into one-dimensional ones, and analyze the possible internal structures on the one-dimensional formulas when the characteristic is $0$.
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Additional Information
  • Zoé Chatzidakis
  • Affiliation: Université Paris 7, Case 7012, 2, place Jussieu, 75251 Paris Cedex 05, France
  • Email:
  • Ehud Hrushovski
  • Affiliation: Institute of Mathematics, The Hebrew University, Givat Ram, Jerusalem 91904, Israel
  • Email:
  • Received by editor(s): August 14, 1996
  • Published electronically: April 8, 1999
  • Additional Notes: The second author was supported by NSF grants DMS 9106711 and 9400894
  • © Copyright 1999 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 351 (1999), 2997-3071
  • MSC (1991): Primary 03C60; Secondary 03C45, 08A35, 12H10
  • DOI:
  • MathSciNet review: 1652269